High-Brilliance Ultranarrow-Band X Rays via Electron Radiation in Colliding Laser Pulses

A setup of a unique x-ray source is put forward employing a relativistic electron beam interacting with two counterpropagating laser pulses in the nonlinear few-photon regime. In contrast to Compton scattering sources, the envisaged x-ray source exhibits an extremely narrow relative bandwidth of the order of ${10}^{-4}$, comparable with an x-ray free-electron laser. The brilliance of the x rays can be an order of magnitude higher than that of a state-of-the-art Compton source. By tuning the laser intensities and the electron energy, one can realize either a single peak or a comblike x-ray source of around keV energy. The laser intensity and the electron energy in the suggested setup are rather moderate, rendering this scheme compact and tabletop size, as opposed to x-ray free-electron laser and synchrotron infrastructures.

Figure 1

Setup of a relativistic electron beam colliding with a single laser pulse for CS (a) and with CPW (b). The emission spectra for CS (c), for Case I (d), and Case II (e). The electron energy is $ϵ=30\mathrm{m}$ in all cases. $s_i$ denotes the absorbed photon numbers from the laser ${\xi }_i$ ($i=1$, 2), respectively.

Figure 2

The angle-resolved spectra: (a) CS; (d) CPW Case I. The angle-integrated spectra: within $\theta \le 0.2\mathrm{mrad}$ for (b) CS; (e) CPW Case I and within $\theta \le 1\mathrm{mrad}$ for (c) CS; (f) CPW Case I. The spectra from a realistic electron beam (solid) and a monochromatic electron beam (dashed): (g) for CS; (h) for CPW Case I. The $x$ axis in panels (g),(h) has been shifted by the peak energy in (b) and (e), respectively. The electron beam has a Gaussian distribution in both angle ($\mathrm{\Delta }\theta =1\mathrm{mrad}$) and energy (0.01% relative FWHM) domain with central energy $ϵ=20\mathrm{m}$. The pulse length for ${\xi }_1$ is 16 000 cycles, while the pulse length for ${\xi }_2$ is the same as the electron beam length, which is about 750 cycles.

Figure 3

(a) The angle-resolved spectra for CPW Case II. The angle-integrated spectra for CPW Case II: (b) within $\theta \le 1\mathrm{mrad}$; (c) within $\theta \le 2\mathrm{mrad}$; (d) spectrum from a realistic electron beam for CPW Case II (solid) and a monochromatic electron beam (dashed). The electron beam has the same distributions as in Fig. 2 but with central energy $ϵ=30\mathrm{m}$. The pulse length for ${\xi }_1$ is 8000 cycles, while the pulse length for ${\xi }_2$ is the same as the electron beam length, which is about 750 cycles.

Figure 4

(a) Required pulse length $N_1$ of the ${\xi }_1$ laser for different emitted photon energies ${\omega }^{\prime }$ with different harmonic peak widths $\delta {\omega }^{\prime }$ in the spectrum. (b) Optimized angle range ${\theta }_{op}$ for different emitted photon energies ${\omega }^{\prime }$ with different harmonic peak widths $\delta {\omega }^{\prime }$ when we choose the pulse length in panel (a).